a+b=1 a的平方+b的平方=2 a的七次方+b的七次方=

=1-a
a^2+(1-a)^2=2
a^2+1-2a+a^2=2
2a^2-2a-1=0
a^2=(2a+1)/2
a^4=(a^2)^2
=((2a+1)/2)^2
=(4a^2+4a+1)/4
=(4*(2a+1)/2+4a+1)/4
=(8a+3)/4
a^3=a^2*a
=(2a+1)/2*a
=(2a^2+a)/2
=(2*(2a+1)/2+a)/2
=(3a+1)/2
a^7=a^3*a^4
=(3a+1)/2*(8a+3)/4
=(24a^2+17a+3)/8
=(24*(2a+1)/2+17a+3)/8
=(24a+12+17a+3)/8
=(41a+15)/8
同理b^7=(41b+15)/8
所以a^7+b^7=(41a+15)/8+(41b+15)/8
=(41(a+b)+30)/8
=(41+30)/8
=71/8